He measured the height of the box to be 5 in. Then, Stephan drew a line from the center of one of the hexagons to each of its vertices and noticed that all the triangles he created have a height of 7 in and a base of 8 in.
Stephan can use this information to determine the volume of the box.
First, he can find the area of the base of the box, which is the area of one of the hexagons. To do this, he can divide the hexagon into six equilateral triangles, each with a base of 8 in and a height of 7 in. The area of each triangle is:
(1/2) x base x height = (1/2) x 8 in x 7 in = 28 in^2
Since there are six triangles making up the hexagon, the area of the hexagon is:
6 x 28 in^2 = 168 in^2
Therefore, the base of the box has an area of 168 in^2.
To find the volume of the box, Stephan can multiply the area of the base by the height of the box:
Volume = base area x height
Volume = 168 in^2 x 5 in
Volume = 840 in^3
Therefore, the volume of the box is 840 cubic inches.